This article presents a method for determining a minimal realization of an arbitrary positive definite spatial stiffness matrix K through the use of a mechanism constructed of a parallel connection of sprgins. The springs are of two types: simple springs and nonsimple springs. The term simple spring refers to a purely translational or purely rotational passive spring while a nonsimple spring couples translational and rotational components. Any positive definite spatial stiffness matrix can be realized with six such springs. However, simple springs are much easier to implement than nonsimple springs. Thus, one generally wants to minimize the number of nonsimple springs. This article presents a method for minimizing the number of screw springs requried while keeping the total number of springs to be six.
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